“System” is not Dorico-specific terminology. Elaine Gould’s “Behind Bars” doesn’t bother to define it, but does bother to define “System Dividers”, which are the two diagonal lines that are often inserted in the gaps between two systems.
A vertical line drawn to the left of multiple staves creates a system, indicating that the music on all the staves is to be played simultaneously. A bracket is an additional vertical line joining staves to show groupings of instruments that function as a unit, such as the string section of an orchestra. A brace is used to join multiple staves that represent an instrument, such as a piano, organ, harp, or marimba. Sometimes a second bracket is used to show instruments grouped in pairs, such as the first and second oboes or first and second violins in an orchestra. In some cases, a brace is used for this purpose.
When more than one system appears on a page, often two parallel diagonal strokes are placed on the left side of the score to separate them.
It’s a single run of bars from one side of the page to the other.
In an orchestral score, you might only get one system to a page. Here’s an example of that, showing lots of instruments but all playing the same seven bars:
In a string quartet score, you might get four systems to a page. Here’s an example of that, showing a string quartet all playing bars 1-6, then all playing bars 7-10, then bars 11-14, then bars 15-20:
And on the first page of the 1st Violin part for that same string quartet, you’ll see 12 staves which correspond to 12 systems:
If it were a typical piano score, you might get 10 or 12 staves on a page but only five or six systems, because the top two staves are played simultaneously, the next two staves are played simultaneously etc.